Finite Group Databasebeta

← #11782070

Subgroups — #11782070

Order 1152.

399 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592393C211yesmaximal, characteristic, complemented
2C3×#4688C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590268C211yesmaximal, characteristic, complemented
5C3×#4458C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#70869—31nomaximal
9#68584—31nomaximal
10#64083C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×ΓL(1,𝔽25)—21no—
13C3×C4×D12C2211yescharacteristic
14C2×#3714—21no—
15C32×C4×C8C2211yescharacteristic
16#63648—21no—
17#63648—21no—
18C3×(C2×D3)⋊C8—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63573—21no—
23#63564—21no—
24#63563—21no—
25C3×#436—31no—
26#5015—31no—
27#5008—31no—
28#4843—31no—
29#4842—31no—
30#4694—31no—
31#4694—31no—
32#4694—61no—
33#4688D311yescharacteristic, complemented
34C3×#335—31no—
35#4485—31no—
36#4485—31no—
37#4481—31no—
38#4481—31no—
39#4458D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C32×C8D411yescharacteristic
47C2×C32×C8D411yescharacteristic
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C3×ΓL(1,𝔽25)—42no—
57#3714—42no—
58#1697—91noSylow
59C2×C3×M16—61no—
60C3×C4×D4—31no—
61C2×#213—61no—
62C2×D24—61no—
63C2×ΓL(1,𝔽25)—21no—
64#874—31no—
65#874—31no—
66#874—61no—
67C4×D12C2×D311yescharacteristic
68#869—31no—
69#869—31no—
70#869—61no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C22⋊C8—61no—
75C3×C4×C8—21no—
76C3×C4×C8C2×D311yescharacteristic
77C3×C4×C8C2×D311yescharacteristic
78#832—61no—
79#821—62no—
80#821—62no—
81#821—61no—
82#821—61no—
83#821—61no—
84#821—61no—
85#821—61no—
86#821—61no—
87(C2×D3)⋊C8—21no—
88#817—61no—
89#809—61no—
90#808—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C22×C3⋊D3—41no—
95C22×C3×D3—21no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—81no—
105#634—81no—
106C2×C3×Dic3—21no—
107C3×D12—21no—
108C3×D12—21no—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111C32×C8—21no—
112C32×C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#486—91no—
117#476—91no—
118#459—91no—
119#436—31no—
120#335—31no—
121#333—91no—
122#331—91no—
123C2×C3×D4—31no—
124C22×C3×C4—61no—
125C2×D12—62no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—121no—
133C2×D12—121no—
134C2×D12D1211yescharacteristic
135C2×C4×D3—21no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—121no—
139C3×M16—122no—
140C2×C3×C8—21no—
141C2×C3×C8—21no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C2×C3×C8D1211yescharacteristic
146C2×C3×C8D1211yescharacteristic
147C2×C3×C8#6711yescharacteristic
148C2×C3×C8#6711yescharacteristic
149C3×C4⋊C4—31no—
150C3×C22⋊C4—61no—
151C3×C42—21no—
152C3×C42C22×D311yescharacteristic
153C3×C42C22×D311yescharacteristic
154#213—122no—
155(C2×D3)⋊C4—21no—
156C4⋊Dic3—62no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—121no—
162C4⋊Dic3D1211yescharacteristic
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166D24—122no—
167ΓL(1,𝔽25)—42no—
168C22×C32#12111yescharacteristic
169C2×C3⋊D3—81no—
170C2×C3⋊D3—81no—
171C2×C3⋊D3—81no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C2×C3×D3—41no—
175C32×C4—21no—
176C32×C4#13511yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C32×C4#13711yescharacteristic
180C3⋊Dic3—81no—
181C3×Dic3—41no—
182C2×D8—181no—
183C2×M16—61no—
184C4⋊Q8—91no—
185#127—91no—
186C4×D4—31no—
187#106—181no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191#102—181no—
192#102—181no—
193#102—181no—
194#102—181no—
195C22⋊C8—61no—
196C4×C8D3211yescharacteristic
197C23×C3—61no—
198C22×D3—21no—
199C22×D3—122no—
200C22×D3—121no—
201C22×D3—121no—
202C3×D4—61no—
203C3×D4—61no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—61no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4C2×D1211yescharacteristic
211C2×C3×C4C2×D1211yescharacteristic
212C2×C3×C4#23511yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4#23911yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×Dic3—21no—
217C2×Dic3—122no—
218C2×Dic3—121no—
219C2×Dic3—121no—
220D12—21no—
221D12—21no—
222D12—122no—
223D12—122no—
224D12—121no—
225D12—121no—
226D12—121no—
227D12—121no—
228D12—121no—
229D12—121no—
230D12—121no—
231D12—121no—
232D12—241no—
233D12—241no—
234D12—241no—
235D12—241no—
236D12—242no—
237C4×D3—41no—
238C4×D3—41no—
239Dic6—242no—
240Dic6—241no—
241Dic6—241no—
242C3×C8—21no—
243C3×C8—21no—
244C3×C8—21no—
245C3×C8—21no—
246C3×C8—41no—
247C3×C8—41no—
248C3×C8—121no—
249C3×C8—121no—
250C3×C8—121no—
251C3⋊C8—41no—
252C3⋊C8—41no—
253C3⋊C8—41no—
254C2×C32#46311yescharacteristic
255C2×C32#46811yescharacteristic
256C2×C32#47211yescharacteristic
257C3⋊D3—161no—
258C3×D3—81no—
259C2×Q8—181no—
260C2×D4—31no—
261C2×D4—181no—
262C2×D4—181no—
263C2×D4—181no—
264C22×C4—61no—
265D8—362no—
266M16—122no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—61no—
270C2×C8#62611yescharacteristic
271C2×C8#62611yescharacteristic
272C4⋊C4—31no—
273C4⋊C4—181no—
274C4⋊C4—181no—
275C22⋊C4—61no—
276C42C2×D3211yescharacteristic
277C22×C3—21no—
278C22×C3—121no—
279C22×C3—121no—
280C22×C3—121no—
281C22×C3#89511yescharacteristic
282C22×C3#93011yescharacteristic
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—242no—
287C2×D3—242no—
288C2×D3—242no—
289C2×D3—241no—
290C2×D3—241no—
291C2×D3—241no—
292C2×D3—241no—
293C2×D3—241no—
294C2×D3—241no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—121no—
303C3×C4#90411yescharacteristic
304C3×C4#90811yescharacteristic
305C3×C4#90811yescharacteristic
306C3×C4#90911yescharacteristic
307C3×C4#91111yescharacteristic
308C3×C4#91811yescharacteristic
309C3×C4#93211yescharacteristic
310C3×C4#95011yescharacteristic
311Dic3—41no—
312Dic3—242no—
313Dic3—241no—
314Dic3—241no—
315C32#169711yescharacteristic, complemented, Sylow
316C23—61no—
317C23—361no—
318Q8—721no—
319D4—61no—
320D4—61no—
321D4—361no—
322D4—361no—
323D4—361no—
324D4—361no—
325D4—721no—
326C2×C4—61no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4—361no—
330C2×C4#379911yescharacteristic
331C2×C4D3×D1211yescharacteristic
332C2×C4C2×#62611yescharacteristic
333C8—21no—
334C8—21no—
335C8—121no—
336C8—121no—
337C8—121no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—241no—
342C2×C3#484411yescharacteristic
343C2×C3#488611yescharacteristic
344C2×C3#489711yescharacteristic
345C2×C3#501611yescharacteristic
346C2×C3#513411yescharacteristic
347C2×C3#514211yescharacteristic
348D3—81no—
349D3—482no—
350D3—481no—
351D3—481no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22—721no—
356C22—721no—
357C22—721no—
358C22#6390911yescharacteristic
359C4—21no—
360C4—121no—
361C4—721no—
362C4#6379511yescharacteristic
363C4#6380111yescharacteristic
364C4#6382911yescharacteristic
365C4#6383011yescharacteristic
366C3—21no—
367C3#6858411yescharacteristic, complemented
368C3#7086911yescharacteristic, complemented
369C2—241no—
370C2—1441no—
371C2#1059036611yescharacteristic
372C2#1059083811yescharacteristic
373C2#1059092711yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#121
prime radical#10590349C2
hypercenterC4×C8D32
hypocenterC32#1697
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10592393C2semidirect
2. C3×#4688C2semidirect
4. #10590268C2semidirect
5. C3×#4458C2semidirect
6. #10589096C2semidirect
7. #10589091C2semidirect
33. #4688D3semidirect
39. #4458D3semidirect
315. C32#1697semidirect
367. C3#68584semidirect
368. C3#70869semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105923932
C3×#46882
#105903492
#105902682
C3×#44582
#105890962
#105890912
#708693
#685843